J1 J2 model

The J1–J2 model is a quantum spin model like the Heisenberg model but also includes a term for the interaction between next-nearest neighbor spins.

Hamiltonian

${\hat {H}}=J_{1}\sum _{\langle ij\rangle }{\vec {S}}_{i}\cdot {\vec {S}}_{j}+J_{2}\sum _{\langle \langle ij\rangle \rangle }{\vec {S}}_{i}\cdot {\vec {S}}_{j}$

See also

• Spin model
• Heisenberg model (quantum)
• Hubbard model
• t-J model
• Majumdar–Ghosh model

References

• J1–J2 model: First-order phase transition versus deconfinement of spinons Phys. Rev. B 73, 184420 (2006) [7 pages] [1]
• J1–J2 model: Energy, correlations, and order-parameter fluctuations on finite lattices (1992) Phys. Rev. B 45, 7832 (1992) [2]
• Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in 2 dimensions (1989) Phys. Rev. Lett. 63, 2148–2151 (1989) [3]
• On Next-Nearest-Neighbor Interaction in Linear Chain. I (1969) J. Math. Phys. 10, 1388 (1969); doi:10.1063/1.1664978 [4]
• On Next-Nearest-Neighbor Interaction in Linear Chain. II (1969) J. Math. Phys. 10, 1399 (1969); doi:10.1063/1.1664979 [5]